Related papers: Starting CLuP with polytope relaxation

Recent advancements in large language models (LLMs) underscore the need for stronger reasoning capabilities to solve complex problems effectively. While Chain-of-Thought (CoT) reasoning has been a step forward, it remains insufficient for…

We present $\textbf{Platypus}$, a family of fine-tuned and merged Large Language Models (LLMs) that achieves the strongest performance and currently stands at first place in HuggingFace's Open LLM Leaderboard as of the release date of this…

A basic model in sequential decision making is the Markov decision process (MDP), which is extended to Robust MDPs (RMDPs) by allowing uncertainty in transition probabilities and optimizing against the worst-case transition probabilities…

Implicit Computational Complexity (ICC) drives better understanding of complexity classes, but it also guides the development of resources-aware languages and static source code analyzers. Among the methods developed, the mwp-flow analysis…

In this study, we introduce an innovative deep learning framework that employs a transformer model to address the challenges of mixed-integer programs, specifically focusing on the Capacitated Lot Sizing Problem (CLSP). Our approach, to our…

Discrete Combinatorial Problems (DCPs) are prevalent in industrial decision-making and optimisation. However, while constraint solving technologies for DCPs have advanced significantly, the core process of formalising them, namely…

Pre-trained Vision-Language (VL) models such as CLIP have demonstrated their excellent performance across numerous downstream tasks. A recent method, Context Optimization (CoOp), further improves the performance of VL models on downstream…

We study the robustness--the invariance under definition changes--of the cluster class CL#P [HHKW05]. This class contains each #P function that is computed by a balanced Turing machine whose accepting paths always form a cluster with…

We present a novel nonlinear model predictive control (MPC) scheme with relaxed stability criteria, based on the idea of generalized discrete-time control Lyapunov functions. These functions need to satisfy an average descent over a finite…

Many existing models for clinical trial outcome prediction are optimized using task-specific loss functions on trial phase-specific data. While this scheme may boost prediction for common diseases and drugs, it can hinder learning of…

Solving large-scale Mixed Integer Programs (MIP) can be difficult without advanced algorithms such as decomposition based techniques. Even if a decomposition technique might be appropriate, there are still many possible decompositions for…

This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at…

We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…

Large-scale datasets have been pivotal to the advancements of deep learning models in recent years, but training on such large datasets invariably incurs substantial storage and computational overhead. Meanwhile, real-world datasets often…

Multi-Task Learning (MTL) is designed to train multiple correlated tasks simultaneously, thereby enhancing the performance of individual tasks. Typically, a multi-task network structure consists of a shared backbone and task-specific…

Continual learning (CL) enables deep networks to acquire new knowledge while avoiding catastrophic forgetting. The powerful generalization ability of pre-trained models (PTMs), such as the Contrastive Language-Image Pre-training (CLIP)…

Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…

This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…

In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our…

We propose and analyze a stabilizing iteration scheme for the algorithmic implementation of model predictive control for linear discrete-time systems. Polytopic input and state constraints are considered and handled by means of so-called…